whatFive hundred points carried by three small equations -- Lorenz's 1963 weather, reduced to a butterfly. Trails fade behind them; one reference point wears a dot, and its shadow twin, born ten-billionths away, wears a ring.

whyThe claim, in four measured parts: the flow is bounded (the radius ledger tops out near fifty and stays); it never repeats (the closest return to two thousand remembered states stays strictly above zero); the wing-switches are unpredictable (the twin diverges at the measured Lyapunov rate, near 0.9 per time unit, and after that its wing choices agree with the original about half the time -- a coin); and the attractor attracts: click to scatter a cloud anywhere, and watch its measured distance to the remembered set collapse from tens of units to about one -- the sampling resolution of the remembered set itself.

howFourth-order Runge-Kutta at a fixed step, seeded starting points, a slowly turning projection. Recurrence skips the youngest memories so the measurement cannot cheat; the cloud's distance is to remembered attractor states, not to other points. The print takes a fresh five-thousand-step exposure of the reference orbit from the live state.